The following description sets forth the inventor's knowledge of related art and problems therein and should not be construed as an admission of knowledge in the prior art.
The gear terms used above will be described with reference to FIG. 12. FIG. 12 is an enlarged perspective view of a tooth profile. The name of each part of the tooth profile is defined as follows. That is, a helical tooth 1 includes a top land 11 (area between symbols A and A′), tooth surfaces 12 (area between symbols A and B) at the left and right sides of the top land 11, bottom lands 13 (area between symbols B and B′), tooth end faces 14, and a tooth root 16. Symbols A and A′ indicate the points at which contact with the mating gear finishes, and these points are at the boundaries between the top land 11 and the tooth surfaces 12. Symbols B and B′ indicate the points at which contact with the mating gear starts and which correspond to the tooth root 16, and these points are at the boundaries between the tooth surfaces 12 and the bottom lands 13. Each tooth surface has a mating pitch point P at a position between symbols A and B, and the diameter of a circle that connects the mating pitch points P of each tooth is referred to as a mating pitch circle diameter. The deepest point of each bottom land 13 in the area between symbols B and B′ is indicated by symbol D, and the diameter of a circle that connects the points indicated by symbol D of each tooth is referred to as a bottom land diameter (R). The diameter of a circle that connects the points indicated by symbols B and B′ at the tooth root of each tooth is referred to as a true involute form diameter (TIF). There is the term “standard pitch circle diameter”, which is similar to PCD. This term means the product of the number of teeth and the transverse module of a gear, which is specific to the gear and is independent of the mating gear. In contrast, mating PCD is the diameter of a circle that connects points, each of which the center-to-center distance between mating gears is divided in a ratio inverse to the number-of-teeth ratio. The gears mesh with each other at the mating pitch points P on the mating pitch circle, and are rotated in a rolling motion without a sliding motion being caused. The contact pressure is at a maximum when the gears mesh with each other at the mating pitch points P, which leads to problems of flaking, such as pitting, and reduces the life of the gears. The minimum radius of curvature is the smallest radius of curvature among a plurality of surfaces in an area around each mating pitch point P. The area between symbol B at the tooth root and symbol D at the deepest point is referred to as an area around the tooth root.
Conventionally, gear teeth have been formed into desired profiles by a cutting process. First, gears having a cycloid surface which were used in the pendulum clock invented by Huygens and which caused small rotational angle errors were used in the field of transmission mechanisms. However, although such a cycloid gear had a small rotational angle error and was suitable for use in clocks, a cutting tool having a complex shape was required since the gear included complex surfaces. In addition, it took a long time to cut each tooth. As time went by and demand for mass production of power transmission gears grew with the industrial revolution, cycloid gears, which were not suitable for mass production, disappeared. Instead, a gear generating method using linear cutting edges, which is suitable for mass production, has been developed. With this method, gears having a tooth surface formed of an involute surface and a root area formed of a trochoid surface can be generated. A cross section of such a gear taken along a plane perpendicular to the gear axis is illustrated in FIG. 13. Most of the gears that are in practical use today are formed by this method. The tool used in this method is a simple, linear rack cutter, and therefore the tooth surface is limited to being an involute surface and the bottom land is limited to being a trochoid surface; it is not possible to form other types of surfaces. A method for producing a gear by the gear generating method using linear cutting edges according to the related art will now be discussed. With this method, the tooth thickness can be easily changed by adjusting the cutting depth of the cutter, and the tooth root strength can be controlled accordingly. In addition, the involute surface can be formed with the linear rack cutter, which can be easily manufactured. With the thus-obtained involute gears, backlash can be maintained at a constant level even when the center-to-center distance between the mating gears varies, and the impact of vibration and sound can be reduced. In addition, the gears can be meshed with each other irrespective of the specifications thereof if the gears have the same normal pitch. The gears having the involute surfaces are advantageous in that the gears can be shifted while in use and can be arranged to appropriately mesh with each other by slightly changing the center-to-center distance between the gears. However, when the gears having the involute surfaces mesh with each other, rotational motion of the gears includes rolling and sliding. Therefore, rotational angle errors occur during the rotational motion including sliding and noise is easily generated as a result of sliding between the involute surfaces. In addition, since the tooth surface is formed of an involute surface, Hertzian stress cannot be minimized at an area around the meshing point. Accordingly, fatigue strength against contact pressure is low.
Further, in the involute gears formed by the gear generating method using linear cutting edges, the bottom land is limited to being the trochoid surface. Therefore, there is a geometric limit to how much the radius of curvature in the area around the tooth root can be increased. In particular, transmission gears used in automobiles are required to have a high tooth root strength. Therefore, owing to stress concentration that occurs at the tooth root portion, it is difficult to satisfy the demand for reduction in size and weight of transmissions with the gears formed by the gear generating method using linear cutting edges. On the other hand, even with the recent progress in the numerical control (NC) processing technology, it has been difficult to manufacture a gear cutting tool for forming surfaces other than the involute surface or the trochoid surface. However, when gears are formed by forging, a die having a surface of any shape can be manufactured, owing to the progress in the NC processing technology. By performing forging using such a die, a free-form surface other than the involute surface or the trochoid surface, or a three-dimensional surface may be obtained. In gears used in clocks, the tooth surface and the bottom land are both formed of a cycloid surface. In gears used in pumps, the tooth surface and the bottom land are both formed of a trochoid surface.
With the recent progress in die manufacturing using the NC technology, the following proposals have been made in which the shapes of the tooth surface and the bottom land are designed to increase the gear strength. That is, for example, an involute gear has been proposed whose tooth strength is increased without degrading the rotation-transmitting function thereof. In this gear, the entire area of each tooth surface is divided into a band-shaped contact area, which includes a trajectory of a contact point between the tooth surface and the mating tooth surface and that extends along the trajectory, and a non-contact area that is positioned outside the contact area. The contact area is formed as an involute helicoid surface and functions as a tooth contact surface which comes into contact with a tooth surface of the mating gear. The non-contact area is formed into a shape such that the non-contact area does not come into contact with the tooth surface of the mating gear. The shape of the non-contact area is obtained by changing a basic shape of the tooth surface, which is the shape in the case where the entire area of the tooth surface is formed as an involute helicoid surface, in a direction such that the tooth strength of the involute gear directly or indirectly increases. For example, the tooth tip is recessed with respect to the basic shape of the tooth tip at both ends thereof in the face width direction, and the bottom land is formed so as to protrude with respect to the basic shape of the bottom land at both ends thereof in the face width direction (see Japanese Unexamined Patent Application Publication No. 2004-360877). As another example, the following proposal has been made with regard to the shape of the bottom land. That is, to provide a high strength gear having a high tooth root strength, according to a first aspect, an involute gear or the like includes a tooth root portion having a profile that is not based on the tooth profile generation theory. According to a second aspect, the bottom land is formed of a bottom land surface that is not based on the tooth profile generation theory and with which stress concentration can be reduced. According to a third aspect, the tooth profile is formed by performing a forging step and then performing steps including a cold pressing step and a sizing step. According to a fourth aspect, the tooth profile is asymmetrical in the left-right direction with respect to the center of the tooth profile or the center of the bottom land. According to a fifth aspect, the bottom land is shaped such that left and right sections thereof with respect to the center of the tooth profile or the center of the bottom land have different shapes. According to a sixth aspect, a continuous fiber flow (fiber structure) is formed in the tooth by the forging step, the cold pressing step, the sizing step, etc. (see Japanese Unexamined Patent Application Publication No. 8-105513).
The above described gears according to the related art have the following problems.
That is, with regard to the tooth surfaces of the involute gears, since the involute gears that mesh with each other rotate while the involute surfaces slide along each other, rotational angle errors occur. In addition, since the involute surfaces slide along each other, noise is easily generated and the involute surfaces are easily worn away. In addition, since the tooth surfaces are formed of the involute surfaces, the radius of curvature cannot be increased and the Hertzian stress is maximized in the area around the meshing point. Therefore, the fatigue strength against contact pressure is low. With regard to the bottom lands of the involute gears, since the bottom lands are formed of the trochoid surfaces, there is a geometric limit to how much the radius of curvature of the bottom lands can be increased. Therefore, stress concentration occurs at the tooth root portion and the fatigue strength against bending is low. For the above-described two reasons, it has been difficult to satisfy the demand for reduction in size and weight of transmissions with the involute gears formed by the gear generating method using linear cutting edges. In addition, it has also been difficult to reduce the gear noise.